Consider the integral | 52 5x? (x3 + 1) dx. In the following, we will evaluate the integral using two methods. A. First,

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Consider The Integral 52 5x X3 1 Dx In The Following We Will Evaluate The Integral Using Two Methods A First 1 (138.7 KiB) Viewed 34 times

Consider the integral | 52 5x? (x3 + 1) dx. In the following, we will evaluate the integral using two methods. A. First, rewrite the integral by multiplying out the integrand: | 52° (n° + 1) dx = dx Then evaluate the resulting integral term-by-term: 5x² (x3 + 1) dx = | 53° (z? + B. Next, rewrite the integral using the substitution w = x3 +1: | 52 5 x* (° +1) dx = 1 dw Evaluate this integral (and back-substitute for w) to find the value of the original integral: 5 x²(x + 1) dx | 5 ° zº C. How are your expressions from parts (A) and (B) different? What is the difference between the two? (answer from B)-(answer from A) = Are both of the answers correct?